Topological and conventional phases of a three-dimensional electronic glass
Prateek Mukati, Adhip Agarwala, Subhro Bhattacharjee
Abstract
We investigate a symmetry-protected ${Z}_{2}$ topological electron glass, a glassy equivalent of the ${Z}_{2}$ topological band insulator in crystalline systems, and uncover associated quantum phase transitions in this three-dimensional amorphous network of atoms. Through explicit numerical calculations of the Witten effect, we show that the ${Z}_{2}$ glass is characterized by an anomalous electromagnetic response, i.e., it can host dyons with $\frac{1}{2}$ electronic charge. We further study, using a variety of numerical diagnostics including such electromagnetic responses, the phase transitions of the ${Z}_{2}$ glass into a metallic and/or a trivial insulating phase. We find that the phase transitions here are governed by subtle features of mobility edges and ``spectral inversion'' which are possibly unique to structurally amorphous systems. Our results provide a concrete setting to understand the general underpinnings of such phases, where strong structural disorder interplays with symmetry-protected topological order.